Muhtarom Muhtarom, Dwi Juniati, Tatag Yuli Eko Siswono


Beliefs and pedagogical content knowledge (PCK) are two factors influencing teaching practice in the classroom. This research aims to describe the beliefs and PCK of the prospective mathematics teachers and the relationship between the two factors on the teaching practices in the mathematics classroom. Participant in this research includes a prospective teacher who has taken a micro teaching subject and has good communication skill. Data were collected through interview and video analysis on the teaching practice in the classroom. The data obtained were coded, simplified, presented, and triangulated for the credibility and concluded. The result of the research shows that the prospective teachers who hold a constructivist belief view mathematics as a dynamic knowledge which evolves and is regarded as the space of creation for humans. Their beliefs on the nature of mathematics support the belief in the teaching-learning process in mathematics classrooms. Furthermore, a good understanding of the prospective teachers have on the components of the PCK has been sufficient, which can be identified in every step of practical activities in the classroom. More elaboration on the relationship between the belief and PCK is presented in this research.


Beliefs; Pedagogical Content Knowledge; Teaching Practice

Full Text:



Ahamad, S.N.S.H., Li, H.C., Shahrill, M., & Prahmana, R.C.I. (2018). Implementation of problem-based learning in geometry lessons. Journal of Physics: Conference Series, 943(1), 012008. https://doi.org/10.1088/1742-6596/943/1/012008.

Amirali, M., & Halai, A. (2010). Teachers’ knowledge about the nature of mathematics: A Survey of Secondary school teachers in Karachi, Pakistan. Bulletin of Education and Research, 32(2), 45-61.

An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the US. Journal of Mathematics Teacher Education, 7(2), 145–172. https://doi.org/10.1023/B:JMTE.0000021943.35739.1c.

Bal, A.P. (2015). Examination of the mathematical problem-solving beliefs and success levels of primary school teacher candidates through the variables of mathematical success and gender. Educational Sciences: Theory and Practice, 15(5), 1373–1390. https://doi.org/10.12738/estp.2015.5.2573.

Ball, D.L., Hill, H.C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14-46.

Ball, D.L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554.

Barkatsas, A.T., & Malone, J. (2005). A typology of mathematics teachers’ beliefs about teaching and learning mathematics and instructional practices. Mathematics Education Research Journal, 17(2), 69–90. https://doi.org/10.1007/BF03217416.

Bazeley, P. & Jackson, K. (2013). Qualitative data analysis with NVivo. Los Angeles: Sage Publications.

Bazeley, P. (2007). Qualitative data analysis with Nvivo qualitative project book. Thousand Oaks: Sage Publications.

Belbase, S. (2012). Teacher belief, knowledge, and practice: A trichotomy of mathematics teacher education. Retrieved from https://files.eric.ed.gov/fulltext/ED530017.pdf.

Beswick, K. (2003). Accounting for the contextual nature of teachers’ beliefs in considering their relationship to practice. In Mathematics education research innovation, networking, opportunity: Proceedings of the 26th Annual Conference of the Mathematics Education Research Group of Australasia (vol. 1, pp. 152–159). Geelong: Pymble N.S.W. MERGA Inc.

Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17(2), 39–68. https://doi.org/10.1007/BF03217415.

Beswick, K. (2012). Teachers’ beliefs about school mathematics and mathematicians’ mathematics and their relationship to practice. Educational Studies in Mathematics, 79(1), 127–147. https://doi.org/10.1007/s10649-011-9333-2.

Black, J.W. (2008). Content knowledge and pedagogical content knowledge of algebra teachers and changes in both types of knowledge as a result of professional development. Proceedings of the 5th Annual TEAM-Math Partnership Conference Pre-Session (pp. 30–40).

Boz, N. (2008). Turkish pre-service mathematics teachers’ beliefs about nature of mathematics teaching. Australian Journal of Teacher Education, 33(5), 66-80. https://doi.org/10.14221/ajte.2008v33n5.5.

Buehl, M.M., & Fives, H. (2009). Exploring teachers’ beliefs about teaching knowledge: Where does it come from? Does it change? The Journal of Experimental Education, 77(4), 367–408. https://doi.org/10.3200/JEXE.77.4.367-408.

Dossey, J. A., McCrone, S. S., & O’Sullivan, C. (2006). Problem solving in the PISA and TIMSS 2003 assessments. Technical Report NCES 2007-049. Washington DC: US Department of Education.

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. Science and Technology Education, 35, 99-101.

Felbrich A., Kaiser G., Schmotz C. (2014) The Cultural Dimension of Beliefs: An Investigation of Future Primary Teachers’ Epistemological Beliefs Concerning the Nature of Mathematics in 15 Countries. In: Blömeke S., Hsieh FJ., Kaiser G., Schmidt W. (eds) International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn. Advances in Mathematics Education (pp. 209-229). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-6437-8_10

Fennema, E., & Franke, M. (1992). Teachers knowledge and its impact. In Grouws D. A. (Ed.), Handbook of research on mathematics teaching and learning. New York: Macmillan Publishing Company.

Giovanni, P., & Sangcap, A. (2010). Mathematics-related beliefs of Filipino college students: Factors affecting mathematics and problem solving performance. Procedia Social and Behavioral Sciences, 8, 465–475. https://doi.org/10.1016/j.sbspro.2010.12.064.

Grigutsch, S., Raatz, U., & Törner, G. (1998). Einstellungen gegenüber mathematik bei mathematiklehrern. Journal Für Mathematik-Didaktik, 19(1), 3–45. https://doi.org/10.1007/BF03338859.

Hamrouni, A.D., & Akkari, I. 2012. The entrepreneurial failure: exploring links between the main causes of failure and the company life cycle qualitative analysis using NVivo 7 software. International Journal of Business and Social Science, 3(4), 189-205.

Hawkins, W.J. (2012). An invest?gat?on of primary teachers’ pedagogical content knowledge when teaching measurement to years three and four. Proceedings of the 12th International Congress on Mathematical Education. Seoul: Seoul National University.

Kahan, J.A., Cooper, D.A., & Bethea, K.A. (2003). The role of mathematics teachers’ content knowledge in their teaching: A framework for research applied to a study of prospective teachers. Journal of Mathematics Teacher Education, 6(3), 223–252. https://doi.org/10.1023/A:1025175812582.

Kilic, H. (2011). The nature of pre-service teachers’ pedagogical content knowledge. Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education–CERME7 (pp. 2690–2696). Rzeszów: University of Rzeszów.

Mewborn, D. (2001). Teachers content knowledge, teacher education, and their effects on the preparation of elementary teachers in the United States. Mathematics Teacher Education and Development, 3(1), 28–36.

Moleong, L.J. (2007). Qualitative Research Method [in Bahasa]. Bandung: Remaja Rosdakarya.

Muhtadi, D., Wahyudin, Kartasasmita, B.G., & Prahmana, R.C.I. (2018). The Integration of technology in teaching mathematics. Journal of Physics: Conference Series, 943(1), 012020. https://doi.org/10.1088/1742-6596/943/1/012020.

Muhtarom, M., Juniati, D., Siswono, T.Y.E., & Rahmatika, I. (2018). Teachers’ and students’ beliefs in mathematics at State Senior High School 5 Semarang. Jurnal Riset Pendidikan Matematika, 5(1), 64-72. https://doi.org/10.21831/jrpm.v5i1.18734.

Muhtarom, Murtianto, Y.H., & Sutrisno. (2017). Thinking process of students with high-mathematics ability (A study on QSR NVivo 11-assisted data analysis). International Journal of Applied Engineering Research, 12(17), 6934-6940.

Muhtarom., Juniati, D., & Siswono, T.Y.E. (2017a). Exploring beliefs in a problem-solving process of prospective teachers with high mathematical ability. Global Journal of Engineering Education, 19(2), 130-136.

Muhtarom., Juniati, D., & Siswono, T.Y.E. (2017b). Consistency and inconsistency of prospective teachers’ beliefs in mathematics, teaching, learning and problem solving. AIP Conference Proceedings (Vol. 1868, p. 050014). College Park: AIP Publishing.

Muhtarom., Juniati, D., & Siswono, T.Y.E. (2018). Exploring prospective teachers' beliefs about nature of mathematics. Journal of Engineering and Applied Sciences, 13(10), 3547-3554.

Muzaini, M., Juniati, D., & Siswono, T. Y. E. (2019). Exploration of student’s quantitative reasoning in solving mathematical problem: case study of field-dependent cognitive style. Journal of Physics: Conference Series, 1157(1), 032093. https://doi.org/10.1088/1742-6596/1157/3/032093.

Nizaruddin, Muhtarom, & Murtianto, Y.H. (2017). Exploring of multi mathematical representation capability in problem solving on senior high school students. Problems of Education in the 21st Century, 75(6), 591-598.

Pajares, M.F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307–332. https://doi.org/10.3102/00346543062003307.

Pehkonen, E., & Pietilä, A. (2003). On relationships between beliefs and knowledge in mathematics education. Proceedings of the Third Conference of the European Society for Research in Mathematics Education. Bellaria: University of Pisa and ERME.

Prahmana, R.C.I., & Suwasti, P. (2014). Local instruction theory on division in Mathematics GASING: The case of rural area’s student in Indonesia. Journal on Mathematics Education, 5(1), 17-26. https://doi.org/10.22342/jme.5.1.1445.17-26.

Raymond, A.M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching. Journal for Research in Mathematics Education, 28(5), 550–576. https://doi.org/10.2307/749691.

Shahrill, M., Putri, R.I.I., Zulkardi, & Prahmana, R.C.I. (2018). Processes involved in solving mathematical problems. AIP Conference Proceedings, 1952(1), 020019. https://doi.org/10.1063/1.5031981.

Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004.

Shulman, L.S. (1987). Knowledge and teaching: Foundations for the new reform. Harvard Educational Review, 57(1), 1-22. https://doi.org/10.17763/haer.57.1.j463w79r56455411.

Siswono, T.Y.E., Kohar, A.W., & Hartono, S. (2017). Secondary teachers’ mathematics-related beliefs and knowledge about mathematical problem-solving. Journal of Physics: Conference Series, 812(1), 012046. https://doi.org/10.1088/1742-6596/812/1/012046.

Siswono, T.Y.E., Kohar, A.W., Rosyidi, A.H., & Hartono, S. (2017). Primary school teachers’ beliefs and knowledge about mathematical problem-solving and their performance on problem-solving task. World Transactions on Engineering and Technology Education, 15(2), 126–131.

Stipek, D.J., Givvin, K.B., Salmon, J. M., & MacGyvers, V.L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226. https://doi.org/10.1016/S0742-051X(00)00052-4.

Thompson, A.G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). Reston: National Council of Teachers of Mathematics.

Turnuklu, E.B., & Yesildere, S. (2007). The pedagogical content knowledge in mathematics: Pre-service primary mathematics teachers' perspectives in Turkey. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 1, 1-13.

Viholainen, A., Asikainen, M., & Hirvonen, P.E. (2014). Mathematics prospective teachers’ epistemological beliefs about the nature of mathematics and the goals of mathematics teaching and learning in the beginning of their studies. Eurasia Journal of Mathematics, Science & Technology Education, 10(2), 159–171. https://doi.org/10.12973/eurasia.2014.1028a.

Wilkins, J.L. (2008). The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, 11(2), 139–164. https://doi.org/10.1007/s10857-007-9068-2.

DOI: https://doi.org/10.22342/jme.10.2.7326.185-202


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
Kampus FKIP Bukit Besar
Jl. Srijaya Negara, Bukit Besar
Palembang - 30139
email: jme@unsri.ac.id

p-ISSN: 2087-8885 | e-ISSN: 2407-0610
Journal on Mathematics Education is licensed under a Creative Commons Attribution 4.0 International License

View My Stats